{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 一 多元函数的导数和梯度    \n",
    "### 1.1 标量关于向量或矩阵的梯度\n",
    "假设有函数$L=f(x)$, 其中$L$是标量，$x$是向量。此时，$L$关于$x_i$($x$的第$i$个元素)的导数可以写成$\\frac{\\partial L}{\\partial x_i}$。另外，也可以求关于向量的其他元素的导数，将其整理如下：  \n",
    "$$ \\frac{\\partial L}{\\partial x}=(\\frac{\\partial L}{\\partial x_1},\\frac{\\partial L}{\\partial x_2},\\dots,\\frac{\\partial L}{\\partial x_n})$$  \n",
    "  \n",
    "像这样，将关于向量各个元素导数罗列到一起，就得到了梯度（gradient)。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "另外，矩阵也可以像向量一样求梯度。假设$W$是一个$m\\times n$的矩阵，则函数$L=g(W)$的梯度如下所示：  \n",
    "$$\\frac{\\partial L}{\\partial W}=\\begin{pmatrix}\\frac{\\partial L}{\\partial W_{11}}&\\cdots&\\frac{\\partial L}{\\partial W_{1n}}\\\\\\vdots&\\ddots& \\\\ \\frac{\\partial L}{\\partial W_{m1}}&&\\frac{\\partial L}{\\partial W_{mn}} \\end{pmatrix} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "由上述关于向量和矩阵的梯度可知：标量关于向量或矩阵的梯度，都保持了向量或矩阵的形状这一性质。 \n",
    "\n",
    "### 1.2 链式法则  \n",
    "学习阶段的神经网络在给定学习数据后会输出损失。我们想得到的是损失关于各个参数的梯度。只要得到了它们的梯度，就可以使用这些梯度进行参数更新（就是所谓的梯度下降算法）。神经网络是利用误差反向传播法来求解梯度。  \n",
    "\n",
    "误差反向传播的关键是链式法则。链式法则是复合函数的求导法则，其中复合函数是由多个函数构成的函数。  \n",
    "\n",
    "考虑复合函数$z=g(f(x))$,令$y=f(x)$和$z=g(y)$这两个函数。 则$z$关于$x$的导数可以按下式求得：  \n",
    "$$\\frac{\\partial z}{\\partial x}=\\frac{\\partial z}{\\partial y}\\frac{\\partial y}{\\partial x}$$  \n",
    "  \n",
    "$z$关于$x$的导数由$y=f(x)$的导数和$z=g(y)$的导数之积求得，这就是链式法则。链式法则的重要之处在于，无论我们要处理函数有多复杂（无论复合了多少个函数），都可以根据它们各自的导数来求复合函数的导数。也就是说，只要能够计算各个函数的局部的导数，就能基于它们的积计算最终的整体的导数。  \n",
    "> 可以认为神经网络是由多个函数复合而成的。误差反向传播法会充分利用链式法则来求关于多个函数（神经网络）的梯度。\n"
   ]
  },
  {
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 二 计算图  \n",
    "计算图是计算过程的图形表示，如下所示就是一个计算图：  \n",
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "计算图通过节点和箭头来表示。这里\"+\"表示加法，变量x和y写在各自的箭头上。像这样，在计算图中，用节点表示计算，处理结果有序流动。这就是计算图的正向传播。  \n",
    "  \n",
    "使用计算图，可以直观地把握计算过程。另外，这样也可以直观地求梯度。重要的是，梯度沿着与正向传播相反的方向传播，这个反方向的传播称为反向传播。"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.1 反向传播的全貌  \n",
    "假设现在要处理$z = x + y$这一计算，但是在该计算的前后，还存在其他的\"某种计算\"。另外，假设最终输出的是标量$L$(在神经网络的学习阶段，计算图的最终输出是损失，它是一个标量)。  \n",
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我们的目标是求$L$关于各个变量的导数（梯度）。这样一来，计算图的反向传播就可以绘制成下图：  \n",
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "如上图所示，反向传播用蓝色的粗箭头表示，在箭头的下方标注传播的值。此时，传播的值是指最终的输出$L$关于各个变量的导数。在$z=x+y$这个例子中，关于$z$的导数是$\\frac{\\partial L}{\\partial z}$，关于$x$和$y$的导数分别是$\\frac{\\partial L}{\\partial x}$和$\\frac{\\partial L}{\\partial y}$。  \n",
    "  \n",
    "根据链式法则，反向传播中流动的导数的值是根据从上游（输出侧）传来的导数和各个运算节点的局部导数之积求得的。因此，在上面的例子中，$\\frac{\\partial L}{\\partial x}=\\frac{\\partial L}{\\partial z}\\frac{\\partial z}{\\partial x}$，$\\frac{\\partial L}{\\partial y}=\\frac{\\partial L}{\\partial z}\\frac{\\partial z}{\\partial y}$。"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.2 加法节点  \n",
    "假设处理$z=x+y$这个基于加法节点的运算。根据分析求得$\\frac{\\partial z}{\\partial x}=1$，$\\frac{\\partial z}{\\partial y}=1$。因此，如下图所示，加法节点将上游传来的值乘以1，再将该梯度向下游传播。也就是说，只是原样地将从上游传来的梯度传播出去。  \n",
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "像这样，计算图直观地表示了计算过程。另外，通过观察反向传播的梯度的流动，可以帮助我们理解反向传播的推导过程。  \n",
    "### 2.3 乘法节点  \n",
    "乘法节点是$z = x\\times y$这样的计算。此时，根据分析知：$\\frac{\\partial z}{\\partial x}=y$和$\\frac{\\partial z}{\\partial y}=x$。因此，乘法节点的反向传播会将\"上游传来的梯度\"乘以\"将正向传播时的输入替换后的值\"。  \n",
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.4 分支节点  \n",
    "分支节点是有分支的节点，如下图所示：  \n",
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "严格来说，分支节点没有节点，只有两根分开的线。此时，相同的值被复制并分叉。因此，分支节点也称为复制节点。它的反向传播时上游传递的梯度之和。  \n",
    "### 2.5 Repeat节点  \n",
    "分支节点有两个分支，但也可以扩展称为N个分支（副本），这里称为`Repeat`节点。如下所示：  \n",
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "上图中将长度为D的数组复制了N份。因为这个Repeat节点可以视为N个分支节点，所以它的反向传播可以通过N个梯度的总和求解，如下所示："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "输入x:\n",
      "[[ 1.33197713  1.99633537  1.17922867  0.39771505 -1.95949919 -0.03073779\n",
      "  -0.50290242  0.03378045]]\n",
      "x.shape:\n",
      "(1, 8)\n",
      "repeat后的输出:\n",
      "[[ 1.33197713  1.99633537  1.17922867  0.39771505 -1.95949919 -0.03073779\n",
      "  -0.50290242  0.03378045]\n",
      " [ 1.33197713  1.99633537  1.17922867  0.39771505 -1.95949919 -0.03073779\n",
      "  -0.50290242  0.03378045]\n",
      " [ 1.33197713  1.99633537  1.17922867  0.39771505 -1.95949919 -0.03073779\n",
      "  -0.50290242  0.03378045]\n",
      " [ 1.33197713  1.99633537  1.17922867  0.39771505 -1.95949919 -0.03073779\n",
      "  -0.50290242  0.03378045]\n",
      " [ 1.33197713  1.99633537  1.17922867  0.39771505 -1.95949919 -0.03073779\n",
      "  -0.50290242  0.03378045]\n",
      " [ 1.33197713  1.99633537  1.17922867  0.39771505 -1.95949919 -0.03073779\n",
      "  -0.50290242  0.03378045]\n",
      " [ 1.33197713  1.99633537  1.17922867  0.39771505 -1.95949919 -0.03073779\n",
      "  -0.50290242  0.03378045]]\n",
      "dy.shape:\n",
      "(7, 8)\n",
      "dx.shape\n",
      "(1, 8)\n"
     ]
    }
   ],
   "source": [
    "import numpy as np \n",
    "\n",
    "D,N = 8,7\n",
    "# 输入\n",
    "x = np.random.randn(1,D)\n",
    "# 正向传播\n",
    "y = np.repeat(x,N,axis=0)\n",
    "\n",
    "print(f\"输入x:\\n{x}\")\n",
    "print(f\"x.shape:\\n{x.shape}\")\n",
    "print(f\"repeat后的输出:\\n{y}\")\n",
    "\n",
    "# 假设的梯度\n",
    "dy = np.random.randn(N,D)\n",
    "print(f\"dy.shape:\\n{dy.shape}\")\n",
    "\n",
    "# 反向传播\n",
    "dx = np.sum(dy,axis=0,keepdims=True)\n",
    "print(f\"dx.shape\\n{dx.shape}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "这里通过`np.repeat()`方法进行元素的复制。上面的例子中将复制N次数组x。通过指定axis,可以指定沿哪个轴复制。因为反向传播时要计算总和，所以使用Numpy的`sum()`方法。此时，通过指定axis来指定对哪一个轴求和。另外`keepdims=True`，可以保持二维数组的维度。"
   ]
  },
  {
   "attachments": {
    "image.png": {
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.6 Sum节点 \n",
    "Sum节点是通用的加法节点。这里考虑一个 $N \\times D$ 的数组沿第0个轴求和。此时，Sum节点的正向传播和反向传播图如下：  \n",
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "如上图所示，Sum节点的反向传播将上游传来的梯度分配到所有箭头上。这是加法节点的反向传播的自然扩展。下面，和Repeat节点一样。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "假设的梯度dy:\n",
      "(1, 8)\n",
      "通过反向传播得到的dx:\n",
      "(7, 8)\n"
     ]
    }
   ],
   "source": [
    "import numpy as np \n",
    "\n",
    "D,N = 8,7\n",
    "\n",
    "# 输入\n",
    "x = np.random.randn(N,D)\n",
    "\n",
    "# 正向传播\n",
    "y = np.sum(x,axis=0,keepdims=True)\n",
    "\n",
    "# 反向传播\n",
    "# 假设的梯度\n",
    "dy = np.random.randn(1,D)\n",
    "dx = np.repeat(dy,N,axis=0)\n",
    "\n",
    "print(f\"假设的梯度dy:\\n{dy.shape}\")\n",
    "print(f\"通过反向传播得到的dx:\\n{dx.shape}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "如上所示，Sum节点的正向传播通过`np.sum()`方法实现，反向传播通过`np.repeat()`方法实现。有趣的是，Sum节点和Repeat节点存在逆向关系。所谓逆向关系，是指Sum节点的正向传播相当于Repeat节点的反向传播，Sum节点的反向传播相当于Repeat节点的正向传播。"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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IDgSAQOgJgMaEnilYXHICJElqdIaS0vKlXW+G53mGYQiSxHGcJEmGYeCN0SW/NsCBRSYAGrPIwKG4RSLgdDoNqWm5eQWStHBj3uNj4ThucHCorr4hJzc/SaOPjU9K0uh1+lS9waTVG5I0+kNxiTp9an5hcWNT88jIKEjOeILwedkRAI1ZdlUKAXkJ8DxvtmSmZ2YLwsK+viFJUnt7h9FkiY1PsmRkVVqru7t7SIryOuL/K8syhuEdHZ1l5ZUmc/qhuMSMzOzevv6lbW/5/YM9IBBqAqAxoSYK9sKJgCiK2Tl5qSYzywb/lEqInKRo2lpVnZCkzcrJGxgYnK1USJLU2dWdZs7QaFPqGxqXclEcWF40RJcEmBlHADRmHBD4uNwIIIQKi0t1+lSK8v2sVghiZFk2v7A4IVFTaa2atMkyqzLsY2NFxaXxCckVlVWL3YFGNxx68fZrL7/ovDMue+ijfN/Sywgr2nb/NTeu/aZt3OrNswoMEkc9AdCYqL8EogCALMuV1uokjQ7D8JCE29Pbl5iss1bVhFYPWJYtKCzWpRgXb8ECNGJ49rIb/5tvJzRPnBqzcuWVW2rdkoIGvrrn1BUxJ16woci/NFlI4IGR6CIAGhNd9R3N0TY0NsUnakZGbfOBwHFcvioDqQsnAz4BW4TZCrz1/av/vM6MI9L43PkxMStPue8bzw9eEtrHTl+5IuaMx7SwDNx8LhjICxoD10AUEWjv6IyNT+rrH5hbzDa7PUmjK6+0hrb5MtEZlmVz8wpSUk00Hcr+vYkFSb1FKUV9ErIlrfnjqhUxZzyc4PkNZS5n/XknrFyx+p49/Qu1SsBEb+DIciQAGrMcaxVimppAX/9AbHxSR2dXYBJBEPILiqYfsbfZ7AlJ2jnrU2BxM9xvamrR6gwLLTPqz2COxj7yh5iVMWc+o/f0JYo1m65eGbNy5dVb6mA0ZobVBckmJwAaMzkXOLqMCYyMjMYnJDc0NrtjlCQpPTP7wMG44eGRqaJ2C0z/wOBUCRboeFPzYsgMbVh7ZkzMyj88moS540B9u+88eUXMiX9enw+DMQtUtVFjFjQmaqoaAg0g4HBgicm6Smu1LMu5+YUHDsYdOBhXWFQSkMS/u1QC4/Zg4WUG9e264+QVMSddtaXe02jBNWtgMMZ/AcDefAiAxsyHHuSNYAIURWn1qboUo1tgDhyMOxSXOPFtTYIkE5K0i9+CCSSryozeMNG3wDTz2WcyX7rg+JjVF71RorZaxKGMN647OWblitX37oXBmPlwhbwqAdAYuA6il0BFZZVPYNw7rW3tgTgQQmnmjOaWpV/FubSsoqikLNC3UO6j4ewPH/j76SdfcO19D9x65ZWX/Pm0FepgzFZvuyaUZYGtKCMAGhNlFQ7hegk0t7SOE5gDB+NMaene8+rf+oam9Mzs6ecCBKZfuH1BELQ6w8I0pyRHS0lZKyZyxHB3W8cQ3vS/609aEbP67+9Z+YULCCxHCwHQmGipaYgzkEBXd89EgXEf8b2nieN4QpKWWuDZw4FeTb8/PDKSpNFzfIhv/HTe639fFbPyVM+Av9Sb8Pg5J6w8/vynNZ43Zab3Cs4CgekJgMZMzwfOLkMCTqdTqzdMpTEVlVXqdF6EjGmWcV1nS86ivMJaMMXEhLn6JnXvuPWkFceffdeuRlFxtutfv/b0VSde+OguKzlXi5APCAQSAI0JpAH7UUQAw/CGRrUr7GBsQqDeJCRpEUKdXd2W9MxwwyGKYpJG73B4phiHxD1kL9659qYrLrnq+n9ceukl197/0o6M9klWjA5JWWAkCgmAxkRhpUPIQQQEQejr6y8tq9BoU9xi09vbZzKn9/X1B6ULjw919Q3FCzL4Dwsvh0cFLzsvQGOWXZVCQPMggONEY1NzeYVVo0sJh6H+iaGwLBufkBzyUZmJBcERIBASAqAxIcEIRpYVgcLi0vqGprANqbCopKExfN0LW27g2JIQAI1ZEuxQaPgSYDlObShw4buIis1u1+gM4dnMCt96Bc+WiABozBKBh2LDlUBrW3tBYXG4eufxy2BMG53fjxSEeYDg3rIhABqzbKoSAgkNgeKSspbWttDYWjArpWUVTU0tC2YeDAOBkBEAjQkZSjC0PAgYjGl2+1iYx9Le0Rn+ja0wZwjuLQ4B0JjF4QylRAYBURQPxSX6foBSIkb6ent7e4eJCb+iwjkG+np7+/pszIwik0iXpb6pLfVPaYmzdzfVVNT3BZTkwDBdinFGJS9FIlEUnU52KUqGMsOOAGhM2FUJOLSEBEZtNqPJ4nOAactL+uSJ68445+6dHZLvqKIobNknN5/9h2teOaAvHwg6EZgIYaM2rzYx7XmJnz1+9Tnn3Lk72BJXtv32s06+4eX9KeVTvI6DHHUp791z9o2ftPpLQgjFxict3ErMgWHMYZ8kqUNxiRWVVaA0c6C3zLKAxiyzCl3acJCjOs3SQHh/nVdiMJtt1PvPZnNQnPfUDP2UGNyBExRF4BhGC4oiqp9JiiJxzDFQZTFVO2Zp8DDlNre0lpSWByZCQwd3vvbi36/ZHPiDkFRB4mfrrz3/OfN0k8/QwDcfHxzx+4eGDn7+xouXXv9hrVd4FEWhChM/3XDNOc+nTWdJ4as2XX1zoMYoimK2ZE7zo2qBISz+PklS7rdZQWkWH364lQgaE241EsH+oJGCRGObv4sEUT3WrN3rH1u33VBYUlpSlGdO+nLr1n25vdPeTwMBqBYyd69f89wWTW5FB4YQ0W217Fj/8L+3afKsHTjTrNtv6Q24YwfmndN+VXVtXX1DYFY0dHBfUsnmqy99o9DrNrJnaswlW66bXmOcddvuevCrYI3Zm1yy6bpLXi/yMkL2DK25+KNrD6cx4iQak19Q1NXVHehq+Oz7NAaUJnwqZak8AY1ZKvLLrlxkz/lifynlf25XIxTqvlz3wt5awRctU7d//Yb4Vv8B35kpdoTavevW7bZ67++KUPXF8//2WkRE8d5defbgMqcwNKPDFZVVjU2e32B2Z1A1Rkt07Lj9b8+ZCNchqd+kK8Sbtvo0BjlKDny2Nz5h30evv7LZ3KNqHl2b8M59fzv9kie27dy1N63VJYNo6OBePd6+67YLnzd6LA0YtUV44zavxkgDebtfvOvqB3a2iAppPbTxgWtvetv1Y8eTaUxRcWl7e8eMolr0ROM0BpRm0WsgjAoEjQmjyohoV6Re/ZY9ld4HdE8oUlfyhqc+KaQDIhNq9jz36oEm9a4r9ZZk1WIBAoFs1sySfv+og5qmM2nDE//Ldd+T1R9pbI999entfotU0Y6tKaH7tcbSsopxE5ddGkOh4W8e/vMj8WqrRGzTa62c2OzXGGfaM+fetE0NyRH36IVP6t0rFnMZL/z1nn3j2jF61dKDf304btRlKUVj5cQmn8YoisJXvHPVNZtdvw2Ghr+858LnLaq6TqYxpWUVloysrOzcMNws6ZluXZn4/6G4xEprlSiGsvUZcHnBbtgRAI0JuyqJTIfQqGnz5vRxoyPIZt70+HtmW4CMKFzFjqee21XpasggR2Xs7vgqt8wgW/nBz2Krgk0gW9r7j71l9P2SCRoxvf3Y+2l+iwjL2LY5PWRTjcvKK8f96qVbYxQFNzx9wb27uyW+Wq9rEpVAjVEUkcN7K80J8Ymb7/vLHbv7XPFOoTGKgqc8+5e79qiWdCmqpSCNEavev/Zaj8aMfvXPaTSmpLS8pKy8rb0jDLe6+oaJ6uI+kpGZPQJvj0bml3xuXoPGzI0b5BpHQKjZ++ae6nFdYEzRx89sSOwKbJhIPdrXHv2vztdYcclMnNU+UjZRYFxD4tvXrtuSYDSmubfkT9Y/siGpM8CiUL3vza+DRlDGeTarj5XW6nFLgXk1RmFy1l927daKAq2xR1ICNQY5Cjbdc8/LCY24xOWvv/SOnep5RfFqDHK0NA+pR1x9Zeqq+UzuqxffuKWiUJPqsjSlxox8de80GlNYVNLR0Tmr6BYt8aR9ZaAui8Y/rAoCjQmr6ohcZ7iSz974pjm4A2TCYIyiSH26/z7xlsEnMWrAyJ776asvf1Y4ybCK2rG2bndlwGDMnufXeQdj3LDEpoMbd1aEClx1TV1NbX2gNTRw4AuNq6uOt37wj7/e/q5J7eZSRN94DBo98MDp/zroalpRuifPvXVHa1ZSygDicl695K49/YivPXSoQv3tSjRwYLfWY+n9qy+85X2j25J/PEa12/K/W69xzzzjK96+7M/rXH1l6ryym8bNK8vNL+zu7gl0NXz2x2kMqEv4VM3iewIas/jMl2WJQsWujfsCxvbVoZQJgzGIqNj18sZDTYGjNsheHrsjNi/7m11xnk4zPx+xI3H9E9tyfHOhxY749c8EDMaoKYXarzfuqfHnmd9eZ2dXXkGRzwZZo9n2zHWX3PziJ6lNnCK17XziP2mEgkYrkne+edd5f7rq2U++yu7kWg+tvevpj1OzUw/t+fqjZ6//1xtbE9Q5Cnjhpnsf2XTw6+1fFVMKUav56LlrL7rtxe1Gl6Vdj68346olzc6N9557+rXPfLw/yzWAz1XveOjRDw2F+YYDe1684bTLnvzUXFYe+8Y951xw/zuJlQE6rDeYxhwOn6thtePTGFCXsKqXJXEGNGZJsC+/QqWe5Pc+LQx4E10ZPxiDqDbj9k27C4YCOtRcAhNfow7IIHv5wXEyg0ZM76150zDoHc5xDcZ8EDAYo2Kk8z95VzvF24uzx4wThFZnmH0+BTGjAzZG9ZR3Ov3NOZGwOXytsBmb5fCBfrtTQcTowAjG+K35DbjXIwjbnxUjKQrUxV9b0b0HGhPd9R+66IXa/e8fck/SVRRx0Jqu27HhiSffPWAyW8wmszndrE1IKepx3YW9hUo9lr3xAYP8yF4Ruz/T3Y8m9FszDLs3rn3qra9M5T1OxPVVZuh2vvnE2vf2pVUGvGAjNn2zaX9DgGx5jc/tryzLsfFJ4bywvzuukZFRkzl9bjFCLiCwmARAYxaT9rIuS2iJ/VTnHu5evDjFjsSPE2bxts0MPLNkZA0ODs0g4VImaWxqLiuvXEoPoGwgMDMCoDEz4wSpDk8AOYoOxVaS3p6tw2eYdwqElxzcXxT4hs28TCKERkZGyyus4171n5fRhcmcX1gctpPKFiZisBqpBEBjIrXmwtFvhNek6stHAmYWL6SX4lBpsqEWn7emMYyzrb0jN68gLiHZkJrW29dvSc9cSMfnaxshlJisI0n3u57ztQb5gcCCEgCNWVC80WccUTb30PeCh47o0dFxK9fMvEyE0PDwiLWqxmBMC3xbsLGpGSGUpNFjGD5za4ucsqu7Jz0ja5ELheKAwNwIgMbMjRvkilQCHR2dOXkFsfFJgdLi3j8Ym8By6iyw2rr6casvh1W0ZktGb29fWLkEzgCBqQiAxkxFBo4vTwJd3T0T1cV9JDevwB2z08nGJyTzvPrmZLj9G3M4krUpYTtrOdxwgT9LTgA0ZsmrABxYbALNza2Tykz/wKDPlYLC4nELMPtOLe1OUUlZXX3j0voApQOBmRMAjZk5K0i5fAhU19SNk5kkjT6wcWCz25O1+nD7oUmCJOMTNe4OveVTGRDJsiYAGrOsqxeCm4LA0NDwwdiEQJmpqq4dl7aktLy4pGzcwSX8KMtymiVj3LLQS+gPFA0EZkIANGYmlCDNXAmIDV89e98DDzz8+Jo16vbIww/dd98LXzWKiiLWfbnu/vsefvhR16lHH3vowQcfePFQi3vhFDSQ8uYj/7zvoYfUs2seeHRzJjZXDybJ19PTGxuf1NnVnZtf6JMZklSXRA78JwiCRmcI7EALPLv4+w2NTemZ2bIsL37RUCIQmDMB0Jg5o4OMMyCA8LbCNO1bt/xhRczKFTGn3rgxMTWzsldd1gxhrYWm5LduWr1SPXXKbW8mmDKtfU6PTa63wpy07ZHzT/37mq0HdVkNoyF756altS02Psn9Jr8kSemZ2QcOxk31QkQs8IIAACAASURBVMzw8EiSRs+FweA/juMJSVqKDvy5txnwhyRAYKkJgMYsdQ1EQfl8xduXn6BqzMm3fxH8k5V82ZsXr1Y15sR79w4Ev0yJRlKeuez6rdWBazTPm1VtXX1CosZmt/ssCYJgNFmmeWe+vMKaH7ASsy/jYu5IkmRMs7S2tS9moVAWEAgJAdCYkGAEI9MRQKP77ztR1ZgTL9xQFLgKMbIZnjnvRFVjTrjk9eKgM3bzi5dcu6kicCHn6Yo47DlZlsvKK5O1KTjh+91mTyaWZaf56V9RFE3m9CVcHEySpMzs3ILC4sPGCAmAQBgSAI0Jw0pZdi5xOf85/wS1T2z1/YcCfvEEy3z176edeoq7G+3BuIAX67HsVy679q2SUHUMIYTyC4r0BhPDzEW0BEFYKplxC0x+QVHgnLdld31AQMuZAGjMcq7dcIlN6t558ypVY064/IMq74uNRMGbl1++4ZvNt65Umzgn/WNTrfeHUsj816+6/PWC8e2NOUYjimJGVo7JnD6fFfuXRGZAYOZY5ZAtnAiAxoRTbSxbX5ymZ/64Sm2vnPaUzt04ocvevvrylzIcjOGZ01WNWXn62lT3gD9d8u5Vf/9PZkCrZh5YOI4zpaVnZudO0xs2Q/NumSkpLZekkE1AmKZoluMysnKgBTMNIjgVEQRAYyKimiLdSbFh89UnqRqz6qbtrZKiOCs33XjJ82YbUsTaLf9wNXFW3vRZu+vMB9dd/qI54DeF5x47TTP6FGNBYXGoOpoEQcgvLNalGG02/6yBufs3dc6e3r7EZJ21qiZUnk9dFJwBAgtLADRmYfmCdTcBIv4R1/Tl4897IYPjav930yXP6UdcE8nw+AdPUtsxMee9kslxNVtvvuS5VPeZ+bHDcSJZqy+vsIb8hRKfACxEg4bj+QJVxlIXWsbmRxdyA4GZEgCNmSkpSDcfAnzpm5e5py/fuSv349svezzJO1WZK379ItfUshPv3Z33yS2XPK0ZDp7EPJdibTZ7fKJm4X5qjGXZ3LyClFRTf/9AqDRMkqSOjs4kjaqL8+/Zmws1yAMEFoAAaMwCQAWTEwig4X33rlLHXVad/ue/XvhoXK9vSAMN7LnrZLUb7fizzv/LxWsSgl+gmWBoBgcGBodi45MW4W2Snp5eY5pFqzc0NDbP5z1NhmGqqmsTk7WZWTkjo6MzCBGSAIGIIQAaEzFVFdmOslmvnHO8q0/sTw9+3e1TGEVRuPQXzotxyc8ZDxzqCTwzl4i7urpj45N6FvHnVWx2e0FRSXxCcnFJ2eDg0MxnrzEM09vXn5tXEJ+oKa+wEvC7lnOpcMgT7gRAY8K9hpaJf1L7ZzeuWrni+DPu3tsRrCNS6/YbV8asjPnjffvGnZl16M3NrXEJyUPDI7POOe8MLMvW1TdYMrLiEpI1OkNeQVFDY9Pg4JDNbndgGEEQDgdms9n7+wdq6+qzc/ISk3UJSdqs7NyW1rZwW9153jDAABDwEwCN8bOAvYUkwBif/uOJp9+527PqZUBRdMrTp59wxl1ftHrfjwk4N4vdqurahCTt2FjAS56zyB2ypLIsEwTR2dVdXmFNz8w2paUbUtN0KUaDMc1kTs/MyrFW1fT09tGw8ljIkIOhsCYAGhPW1bOcnGO6K4pbsMnG85mu8inOzCx+WZZLSss1OgMJ3U0zIwapgMCiEQCNWTTUUNCCEJAkKTevwJCa5nR6F21ekHLAKBAAAnMhABozF2qQJ0wICIKQnplttmTyYbD8fpgwATeAQFgRAI0Jq+oAZ2ZBgGXZVJM5OycP3iaZBTVICgQWlwBozOLyhtJCRICiaJ0+tbC4FFZbCRFRMAMEFoQAaMyCYAWjC0rAgWGJybpKa3Wo3rFfUG/BOBCIZgKgMdFc+xEZ+8joaHxCckNjU0R6D04DgSgjABoTZRUe4eH29Q/Exie1d3RGeBzgPhCIFgKgMdFS08sgzo6Oztj4pL7+gWUQC4QABKKEAGhMlFR0xIfZ0Ngcn5A8MgJLRkZ8VUIAUUUANCaqqjtSg620Vicm6xwOLFIDAL+BQLQSAI2J1pqPkLgRQkXFpVp9KkVREeIyuAkEgICfAGiMnwXshRsBSZKyc/NTTWankw0338AfIAAEZkIANGYmlCDNEhDged6cnmnJyIKl75eAPhQJBEJEADQmRCDBTEgJOJ1OgzEtJ69AkoJ/bSakpYAxIAAEFpoAaMxCEwb7syZAkpRGZygpLYd1YmbNDjIAgTAjABoTZhUS9e6MORyJydqq6tqoJwEAgMByIAAasxxqcdnEMDwyEpeQ3NTUsmwigkCAQJQTAI2J8gsgjMLv7e2LjU/q7OoOI5/AFSAABOZHADRmfvwgd4gItLV3xMYn9Q8MhsgemAECQCAsCIDGhEU1RLkTdfUN8Ykam80e5RwgfCCw/AiAxiy/Oo2kiGRZLq+0Jmn0OI5Hkt/gKxAAAjMjABozM06QagEIIIQKCot1KUaaphfAPJgEAkBg6QmAxix9HUSnB6IoZmXnGtMsLMdFJwGIGghEAwHQmGio5bCLkeP5NHNGRmY2rBMTdnUDDgGBkBIAjQkpTjA2AwIMw6SkmvIKimCdmBnQgiRAILIJgMZEdv1FnPcEQSRrU0rLKmRZjjjnwWEgAARmSwA0ZrbEIP3cCdjtYwmJmpra+rmbgJxAAAhEFAHQmIiqrkh2dnBoODY+qaW1LZKDAN+BABCYHQHQmNnxgtRzI9Dd3RMbn9Td3TO37JALCACBCCUAGhOhFRdJbre0tsXGJw0ODUeS0+ArEAACoSAAGhMKimBjagI1tXUJiRq7fWzqJHAGCACBZUsANGbZVu2SBybLcll5ZbI2hSCIJXcGHAACQGBJCIDGLAn25V+oJEn5BUV6g4lhmOUfLUQIBIDAFARAY6YAA4fnQUAQhIysnDRzBgfrxMwDI2QFAsuAAGjMMqjE8AqB5ThjmiUrO1cUxfDyDLwBAkBg0QmAxiw68mVdIE3TuhRjQWExQmhZBwrBAQEgMCMCoDEzwgSJZkIAx/Ekjb68wgrrxMwEF6QBAtFAADQmGmp5MWK02ezxiZq6+obFKAzKAAJAIEIIgMZESEWFt5sDA4Ox8Ult7R3h7SZ4BwSAwGITAI1ZbOLLr7zOru7Y+KTe3r7lFxpEBASAwDwJgMbME2C0Z29qbolLSB4eHol2EBA/EAACkxEAjZmMChybGYGq6prEZO2YwzGz5JAKCACBqCMAGhN1VR6SgBFCxSVlGp2BJMmQGAQjQAAILEsCoDHLsloXNihJknLyCgzGNKfTubAlgXUgAAQinABoTIRX4KK7LwiCJSPLnJ7J8/yiFw4FAgEgEGEEQGMirMKW1l1JklJN5uzcfEmSltYTKB0IAIGIIAAaExHVFEZO9vX1wzoxYVQf4AoQCG8CoDHhXT/gHRAAAkAgkgmAxkRy7YHvQAAIAIHwJgAaE971A94BASAABCKZAGhMJNce+A4EgAAQCG8CoDHhXT/gHRAAAkAgkgmAxkRy7YHvQAAIAIHwJgAaE971A94BASAABCKZAGhMJNce+A4EgAAQCG8CoDHhXT/gHRAAAkAgkgmAxkRy7YHvQAAIAIHwJgAaE971A94BASAABCKZAGhMJNce+A4EgAAQCG8CoDHhXT/gHRAAAkAgkgmEQGO+lYxdmEPCBgSAABAAAkBgHIFvJWN7u7kZquS3JqbDeJRvE2EDAkAACAABIDApgREOTdSOSY9MojGTpoODQAAIAAEgAARmSwA0ZrbEID0QAAJAAAjMlABozExJQTogAASAABCYLQHQmNkSW5r0CMmMJC9N2cunVJkDhgtemzIwXnDGEVXA5BrD4fymZvbdqbf32oSICjP8nEXSB/nkSzaPbLCDzMn5bMOUIiLXN5E/K+WZKeLAeumVBVybN7tEspdZGO38q4jnbzOS7+BeuxNKlyjunkI2X3KdkNGBCvLBXjR+KFBGH+UTz9tlRZF5ScZ5NMyiLkqqx8USu5g+JFjwCVkmFBRwQB7tps+uETyTWmTUTUjVeNBWQyJakUco/0GHOwKev9NIvo5NDAcdLCOubJfccSiK3NxCnWQV8IBSFRE1BpdSjUu1tNdzGekbnV+TPsuytZE8o1bkPRbQF0X43X2yIsms36Y8OMq9P9VXrIUv5DzWEC+V2Kecg1NEeH0IsKytIm/yh+M/EbAn17VQJxRy7T6XA85NsiuJb+QR17T5EE2SxHVI1lXip9X5Ag9MJrcPcx+1sVsn37hMxu/KbK9nEefuK2ELxl95gaW79+WhfubishlHPdEAHJk9gck1Bu+mjsygX29i/9vEvllD31zudO//13Xkvw30SQZ69mUtSA6RR42E1EBIjeqdZcI/WR4g1bMNhNQr+C/iCenGHZAdjCdXCztJLiSgZpfNBhJNfQdWFFnuxsVim2j1fn8kpxjbze3t5vZ2sbek4ZfXu/a7uV3V5E/S6He63B/5Que4QlWN+ZGFWlvDPOvfnJ+rN25FUWR9BX6K/44mNzaTPy/k+oNsyPuKse9qptt+nMuqKiWhDkKqd23V3fSxRnoP5vnoPthA+77Kcmcb+YtCrp9HnbTUQfJ3G4k1A1IH7dn6eZcHsrQ1j/i3TUYs/1AW8adM8s+55OoUbFUufUcZfV8ls7H/sHeuwNqR48uIq9pEVylolOfvSMGOyyDPzvJv5xaz1ZL0bjZ2jIU8O5M4WkvtJsSEPv7reupnJvqdXv6ge+sT6t0yLAoPGokXPDAVRZbezcav7gy6d/MO9vos4hiNuyziWJ1q/MJaQdUMUdpZRhyTyej8tSaX1ROrqvxC+HE+fmeftL+UOLdWGPLUi1xSR/w6l3nD/Z0K/L+RPieFfIvwpONGnGdbiFXmybfTqlw+KLKd9lbTGHuNgXi03/vRW5v1hDQoekjiNufZOuyYdPJvuUHbpZWT3X9llFVLHJWK/9rCpIz7OghiYge3vd2/fVBO/CCNfj3gyPYOoV5Vbzm5DP9TBberc+LG3m4hHh/xXa8zuZ4DLwmFtzlXp9Ia7zNC0LngDxLJXqgLqOvgs/BpIQhMqTFHl7iemkVpcx6+qpRNGOCTXZtuDIkcd1XquPu5TFLC53X0E13T3S8oUviwhrmnmLqulPlPlzjguVnJYxj/Rg3zTBV9Zxnz3oA0zvT0YWM27pUa+jQ9dkQyfnN30H1BUeSODvpYPfZ/evLOWudez9PsFPYE8dCA5P0OovwO57+LiZ9osG8b6H3jvley9GkxfmQy9pNMel09Vz7NlY3EvVbyV8nY39o8jokYt6aUvq2Evq2EOj0FW53n3qdvycW/l0JcpR6nbytldo4XLlVjjsxiNgU9A3LJuCw62L+m4kdqsO/p8WMM+G8L2BZJfDUd+44WOzoFd28XNIqioiBZ5lHAJgqPmohnR/1HRFn9kos4e7YW+00aETPZtiIV+36u91lclt7Jxm/pQT1d9GkWYrUR+44WP8FCnOTdrmuVeFb4uIG5Kg3/S6Vzz5g8OsBcVMyV89KmXOJFu9zRx5yfx1ZMA3BiXfH8HUY8Jg3/gRY/IZ3cMMLfYSC30r7bkzeDLL2bgz80JIuY86wMZ4GNe7CUOlmPrc6n7yr1buXOJAZVNJK/MWBHJGM/NagAr2yT2DHnaRrsB3oPvaMN5Jvupo8kPGSi1LKQ9EYW/rCqFXL/KHtXOh5TyOa7mh2qjuY7c6RxGiNtylXTI1ZYl0M+72m8qhqz2sp3MKhn3Eap7S2fxnhDmvavek26qwz/pQ77bgo+WfWRr7qKpjH2aiP2vRRybbfgn5Y6xN1jwVdbBf+t3lOgXNZK/cZAfYghbSXx61xnrvvRwXUW8eKuRud/GlxbLXWijrij3vmfOvokLXFjnfd4I1+mfq9UjTmlxDlZ74jz2jSPxsz8eg7EMaXGyNLeSurSvMCNPE6HHZtJBh58tt/32BRoFfZDQ2A6jaFFaUcJ8QMjtbZRbdD8t9F5swU/qVbkgjVGovjnSui7S8jfJmOnTN5MVn1FLH97KnZWg8jJcl0nfWwy9vsyvl9WEMNda8Bv6ZYkRU6vIr6TjD84OOGWMX2wEn9/Hn1nOvbdTGdV4NUiia9bmYczsW8bGdPhbmTcKHNmWVBnFNtPX1pKn6bBznLdo30usHbno9XMmRrsWKv3QdV3bsIOYtiLNX6N8Z9H0ls5xHOjnkjZAea4HLYu0Hl/UvX7OVVfGT/mPM3MpPEyLcpj/fRvs9nCPvr3Gc581xFaRInl+BkNqsao/5BMirKnEElYY1KbF0HluDTmnDQmbQpcTB/98zyPxrA250lacovn/i7XNpK/LuPJYHOIFXc2Oa834xdZ2a/sCONRRjsbR4hv5RDPjkimdlZDIkyQPd1CsvRFJXV1tbeHKdiU65Pc0U6trhDsDueZ2S5coqoxH5Bq+L5NVG/+Ho3pbKVOqlarSXQ4zzDRGh5ldnCWgAZHSR1xYpWAqdlVVuc3ibFl+B/rRNcRmeb5fxrJDVNoDI+z56US/2wT/fdlWfowD/9nP3K3Y2ptgn5Q0A9w91vwm1t5dX9Q0A2JPWodqBpzlJm8qpC6etxWQP5eN0uN8bJCLH+H0dcmQCU9nM7fg6cWOjTi/JuRuLNbquigjkujPrSrTz8kzj+SiZ9UzneMuwIRMtSRx6SQL4+4HpIkaUcx/rMM5mtvG8tdLGKFA4MSx3FXptIJoqII3PV66gselQ8Idd6nNkWRjVXEWYXMY9aJG31FBvmy61Kc3fXsjXpKjVHkZncVDAr7q8gfZjGHXFXgrgjf/4UTn1G8luHv/AlMozFcVgN1fbOgb6TOL2GzCPHTcvL8Cr4FKUqwxridkAj2PM10GiPizjM12I8LuWFZUZD4jBn7f1rqM1Z90jxTg/2mUmAV9enviGTsys5xV/rhwpT4+/PZ9E7qKA3+gLdxpCjycC+zrl98I2uixqgP70FGRXFLPn5U8IAH209f3ijsKMS/Y2S0vvuejL6pdibZ2bNnrDGXBGsMkmUxsD0RvC8irwYo8kA3fYq3h2SFAfu2Hl/p/bjKQr7u6ttRv5MWJtslCewgfWy2870y4lZ/e07WlOPnNHraZ+wA/etMp9VN93AagzipbEws9m4lDgmTFb/GyOoYw/9pyC2E+KXrSfYmC7aigFnvfqR1/b+hiW9A6u3e3Vc20s9clqv2zPwhFfu/ZOzbGvzEbFdHTR6zz/0lR+J/MrEf+9pJQTXk/iD3j3DxuMzbnKfmsI2yooj8HXrsSFcT5BjX/z/Ukv8lZI/GDEo7Cgl3g8NQSZxWJ3JqEcSLY77adzUmXCKkKLKuAj+vjr0ng/7SJ0IS/69U8k33LXWydgylCpqiICmukrylU31OGuikflfEpap9ZdynFZSrM4r4pQb7pa9jKt+pU/vo1KJPrpls6EISHvS0Y+SGfvatwG60yfbfauWb3HUqo9gy/DfFXI87PlltP90T1Gcq20fYtz3tdbmum/mjAb+omFqZSvyrQ/RTccFmSP6lPPxHJmqTHSEZtTnETkFWJCmuijxaT9zWLHS6rjrECS9k4Rc2ig42WGM4Ka6SOD6fLeLVayClzfWcOpn/nh74JnbbkDSr69l3gfA254ka7Bgj/jvfZvJ8Qbxp5PYW8qfFPOX9DH8XjcA0GuN+qJf7HfzzOfh3NdiP0+ntQ2K3IKM5aYyiyIO42OhuaIvCfanY/xnoRNeXjXJKQ5LM0vzDFuyobGe274Y+QwwujakVhCfTsB/ncR3uLxiSPrCyVlF6M1BjZOmrCnJ1Dv1cDXNdNnlljUsyRfGdYvK3GuwIE3lTMX13i+fRS9WYJgkfYU7QYJd6R1BFnF3TJDJEoMbI2U3UyQbsx1nOaqRwNvYf6fiPdZ6xZcSwwRojayrw73vHRf5f8vgBkm/r6ThP+XJXG3l0IWcN6E93j4jU4/wD3r6FCd9JtlGSK7qcH3uHahJK8QtaPB2YEzQGv7zW35Ouc91JRZx1t2OYXvrIFOIClyr8LYs4KpXWST6NkccGmZUmYrWB3EKKSe3slgYqRkfe3xI0ovtRh6AO8Lg05sl+sYGVFVHSN1IXlzkfzyEeanJemcdsHZlV16hc1+N8tJJ5qIg4ykjeVcm81sPeGthXhsR/pwdozIDwuJl8j5QlmrvCQD43IBbb+YctxP3dqnaW4OrUALXDKkBjzm+SOEH8opEr9AzV8HcZyPdJNDTGf9Hh/JuBuKeF29XJ3pyGX1zD7eoSWpCCeHFrMfHLLGequ0+VFzZWcV/V+cdjkJO7VIOd3eTriXVf1mrRP5i8Uws/Uutux8hlncwjlczD/o2+wIj9LpcOOMI8Us25nhvk6lbql6nUHu/gnzKJxniKxmhR38k+WUwem4KfmU38Qo+fV8xs7OAtDmnU1Qxs7qZP1mMnFLHpbrkV+TtS8DXq46Gqjo19zkuM2M+LuE5WeCYTv6De1cPG8fdmMqmSKvxPZTNJgqLIKMlKHJvjzOPVgcn8QX73JIMxruGZLl5vE2sZeVbXszsYRXGNxxioj+xiucO3Sb3+JpTqc3Ed8SMzdV8F80DA9nCjECTBPouwEzoCU2tMMbujkjzFTPylmHmnV+wXUdUA92oF9ed04p529h/jx2OUw7ZjAnyWm9upo7TEnT2+wRvZ2uV8oIRcZSKf6Br/PBWQcYpdl8bUIbmphfyBxtP/gw85n+xGCAVrjCQ8YsSOrRQYRWFHVfG4wf3ILwkPpmI/ndiOaZJEWfogBzvC4sxTn9rk1FrmS6csBmmMehvdlIMdkalqjKLIve3UdzWEu4Nlgsb4QpB726gjCzmH74Ci8GPOU41MiqefStWYnwe75EmLxOe8Y6RqFj1+pksJLsrAf5TNNspyVzf9ezOdpN7y5G+K8Uu8o0ETNeb0Itr3ldvi6rgL1Jij812NTkWt3PONQRqTaiXv6OYecI9PKHJvB/WzXHbiJCWJFjZX06elYL/OpP5VSV+cQd7bKg4hlNbCJtAyTfAvFRArMplDvttiAI3JduVem3qf+tRK/jiL+aSTi7dxt02jMUNyezt1SqVgd7DXZBB/SFe3X2ixY8zqzp+K2Tqk3uiPNJIXuQCenoqd1yRJsrSvGF9ZwatdtiJ/cwr1EYPa+pyPVlCrtPiFZczDlfS5BuyUQuZhK7u/z3lNGr66lCsLfDCSpM+L8BO8Y/7sEPM7I35CHtvpvkV7A+M9/Xsot8O5245oEWV2OL8c83T6MYGNeRkNugVMljbnYpe1I6QoiEej/jRyUzd9vAY7IsNZwXI3GbCf6NXt+xrsCJ17Hz+7XuSRtL2UXJ2K/SCFOL+Iea1DqHF1UzKMGN/ufLSY+pMJ/54Gv6YT8ZSwu1/y93wGaYwaAOKlWlpWZJQ/LBYN8V/3TLLt7xN7EModdPclqqhjCp3bXNMBttVSv02jXnNPDWhTx2NecTWjZnU9e0HOZMxfTqnEj/OW7p6ksLWC/GHOJBetzyzshITA1BpTwg85EY7knAbqzEzykiJ6TR2719V7O5O+MonmXyqn7y5zbeVstv+ZQh4aYs61UG+MIP8xTyhyTwf1w2TszPoJZ6aP1aMxisLxd6divyjhh5H0eZUzSx3pDtYYRUGCVDTIbWtmX6+mjkvGzm1y6dw0GqMo9j76Vxp1cFukucfrBVpRJmrMh7l+jemfq8Zww8xxFmee58ahasyR6fQrAb1PnsHVeuYvBtw9D0d97jPRn42qc1uzWqlfqhqjPj8mlhPHFnHtSN5bhP2jQ70lKYoyQWOmG49heumpNUahGTQiesfAFbm4gfxNKu7fDNj3NOrsHd7Orqlx3pWhFjRGcA9mEhcUqMMPF2YQ5+SpO5dmEVc3iZNMJ56uxuWmZvJ35bw6t1i99xGPdHkmpCT3szebAtoxQ7LC87eaaa3vgkLiM5bxfWUrSrkcdYE+4cMi/HzX9YBY/r40/IYuSRS46/TU5+7xIpG/LYX62Okf85co7sYM6pkeSfUEoW7XIz9Hq+3+I3VYjEdj5Mwq4o+17GMW8o2AqRzqMKSF2kWpt+nPC7AbutWdj/Lw2/vU+mvrpE4q8nZ5KXJnJ/UrC5Mrqk8zHo2R0aFS/A9VgntET70MUogHaukTfH2h6tPOJH1lTSO8aYTbWDVxUEQ9srZdxATk8DzlBNTBBI3xn5ORppG+MRP/rpG8rZz+p3e7IVPtZDb6Taka8+sseo1rPObREvJnqeRdnrEZ+txUv8bM/Hr2+TD1eIw3iesp8ArvF8F1VB7poI70PkV508Hf0BOYTmMYRW4YFQpw5JBkBy1m9XOJDtfNagZ9ZRLJrSmk/lHg2oqcRs+XXB4YdF5bzGaoD2XoixL6C16uaqVWGMn1ru8KN8rEJGPfSXfOLlCfxihyST1xhJZ8vdu5xj2XP1hjWIy7UX3qZC0kYkn2fM1EjZHrRj2+uvvK1A9IfCUd+16W88sG5iPXCOr0GjPndgzdSx+dxdZ7n3bxMf6dKfuvuVTXGMYkfQuu7IgT9vWIDhl9lu+6f7mAzlZjfmqhX3U58GYNtSKor8xlzjc+ocg9JPK/uyOImwvw44s514xVT1+ZOrlAEp60UJ+4qn5XkftGL+fXEJe2SV5VRbXDfOKo/7Y0+WUgo0/zsSN0xBNDCLnufWcU0jcXe7cSZzzjHY8Z8hT6jk3MGBHSR4T0Ye42E3F3h2t/RKzj0MS+Mlfxsn2U3+9AEstdoaf2ua4ItUlqoONdDy7eeWVeB2WUWk38tpBrd7CXpeJnVfGJtZ6+MsSpg/CvjMnlDeTvSvgBb+UqipxXR/4mj62XxmuMSHJXpBLrvPNBEMPfnIrf2uN6UPBpjKJIDH+7Cb++09UFh6QyB2JGmRMPozGqwxLFXpBCvtTjncPtncz9VTX54wLO7o0p6O80GuNKhxj+bjNxb6/kas7JI6POvxqJxwc9DzeuJKrGnFjKxvbz8f38oWbqyHru/QAACPNJREFU9xb6f33qfnwfe4c5QGOCxhddz0yKMun17PPwsBojkexf9d5xNU829UnlqBJ+VrNYfSXCzswJTKsxspTQwNxaQJ6VTpyUTl5aRD9Rz+opeSbtmMk8kHsHmD+m4Gflq8JzRR55nIXJkuSUCvz/kvF7XNMHHb30UcnYz4oD+x0mszTumHs8xnWjQgx3lR77volJcNsI0hi5sJb4joZ836UTvN25WoOd423HrDFiPy7haST9t9SjcK4xf3cfutrA+mkytqKCH3MVPUFj0P/y1HaMa1abnGYlvq0hNrimSs+gr0wewITMUSFrmF+fhx9T6no8V0uRizucn9iRxIp7u9WXKhAnftzI16ij6MjS7Nzu7VsIHvP3fCc9hGS0NQ+/09vlPCuNEXH+jYAm1IZmdWDZP+av3qu87RhB+Hc6/vtcZtsIYnjxrTx8ZSnX6FMK75i/qjFp+OocdZz/JAN2XJa6c5YJv9inMS4tPyLbOzd6XC17P3IO51mp1LYe5iQznUhPN3f51iZuSwO1ykC/3kxfmU9doW5kjA47Idu1X0C/Z59KYzyFqdMC3bqiKGO99K9y2Bb16cg3d9mVDEmxVuJX6UwSIyNO+KRDxGTv3GUZpVURxxRwXWr18fe5JMF/cYvif7KIBwekz4LaMWqWc+pFz71PlnYW4b8r5Xvd4hSgMYoijw0zpxrIDd43e7gZa8yFqXSyr4K8YJke6qdz1RhFUcgx9goTcWUjv7+RWm0k1/a79cZrXZHtmHDA26X2ZSP1OzO9qdvbw9YrWF2NxamemTxWgq9nn+nDaIyMEsrxo/O54L5KOaeaOG4GU0N9pcDO3AhMrTHFvD1gPijFSVWj/N42zkjJNMMFjcdI4vtl9B1F5G+02DEZ1B2l9CuTzTcXCfYCHfatZP/23Ty2W1Ykmn+hmLqh0rmxkbnSjK8udKb6ZvUcPiZ5dNB5ZxF5nIG4rITZofZFyJZq4i+N6nQdEeceK6XOSsW+l0JcVkK/NyqzOHdfFr4yj3mlwflcPftSEX6MmXxIfRKUi1uo1Wbytgr63hZRkVFKI31DNn5MOnWrlVNHWURhbQa5UZUNubqTuaOQ/LUWO8pC3VbGuuZ0yd19zNkm8tZa5ys1zIYK8vvJ2PF5zlRW/LCEPFaLHZtFbxo/S9g3HiMXNpArjPjvTcSZBc44yvOgK5Hspank+4SMnNyVBupjRlbUOVHuid1ybTP56zyuRXYN4aQQF7ue4m/MIY5095V5uSGWv9dEPKu+/yhljwipTdTPzPSuYddT/BB7Yyp+R7v7id7zXN/Iy77xGK+NoL9kD320d+6yX2NcPUW5HcwVZvyXBuzn+VxD4P1Llra43sGcSTumuI/b2e9pRwYV7Psgihuz8XMbRU5GadXkLR1s0HiML5lr7vK9jex9pcz6Psn/SxeT9ZUdZVbnetxcTF2Y5hqP8RlR5OF++jgLo/ZeqlHgF7pnTwRoDI7zT+Xgx+Y5M93jJZ68Ho2p7qR+l0Ju8nSRyaNDzB9SiFs7RMxbBC/K4sS+MiR7B2Pkjg7qGDOj9RlX30nC/u7v85FLG8mYIq7bddW4NcaCCZ5G2wj/eAZ+eZOvij0zbiSKXQCNkUcIYXcV+VPXF/xsK6cfkzBP+9QVLRK3VXjfTCql7ywgjjKQ1/neVSqlH2pXv7PqeMwMrmdFRNXeGY/FY2JBF31cCrXZ5p8G6ZoPKXWrvYuoqIk6JoX6MKCjUnVIEF/Nwv7c7BsS9lYJ/A01gSk15vs6fMVkb+Gp73aZ8B+F+D1/meNRGyl53gwPdZDj7IkiwtxTTsedUOa3JpgskzyikKJIsp2XmXHToyeUNXHM359ERnuL8dVVruVMZLQtD3fdVuT2VmpFGa9OExCEx8zEI0OueTgmeptLNozNnvEYbtT5J6M6OvIzHRZTzDUghbez9/h6k6baKWE+w6bQGCR+UESel0WuMmArq9wzrgLaMT6/JZTdzlxkwk8sYotdSiFR3KN55O9T1FdY3O2YGNc7+WdmqC/8n51FnpyK+dsxPjtT7sj1zeSKAq7Op2Eif1cK9kPX+LZ7lPsneuwoC5Mhet6PGW9pMo35fQlncvWkvVPgHo+RM2uJY13DSz/SETd3qI8g1S3kL8xMqrdxrPaVDUoJ1eRvUogbm4QJz1SqxhxfQJ2tV7uPfM6qLwX3Maen0fso4ZVM3OfwDzXYd10j8z/UYN/zDNFjP9HjZ9WLiijVuR47OBt7TS55URZxlJZ4xtuNpkYny6y3ALfGfNbs7TYcV9Gu+vX0lWnxE138A9dHOCsN//5s2zGCuKOWuTWfXJ2KH2Mh76hh48ak5lHuDSt1vhn/vhb/vYX8a5HTxIo7qgNnxzEPFxNHp5K3++fLqWef6RLd44uHvZ7FgEkc7qkck/yfQX3gkBKsxE9TyBeGPL12jh76ZzrsqBT8p1rsmGzn+GULxl8u8DkEBCbXGA7j3+4dN9UyoDBR3Nfib/EHnIDdWRBwjLCPt3m7RMbnkwfGhCrvq4ljtHcVECR7ucsOp7p2DuJE/YDonlOKeKkIc42LeNeDaXPK3vvP+AKm+ox4yTggTngLVm6zC8YRIdch+VdLkCV9O1/iVRy/QUFKHfLOSBaljH4+k0CqGzKydPLWoFaK3D/KfeO36Lcx5R5CjiALUySUkanFOe5VQTWpjNI6uAx/Q1ntwNE63DcgeYz0rPrDcZ6VhAa86w+xhKD1zUyQUV4Xl0LJXSN85uSv78m9Q+x7/VIbibz15feTnfz5xp9g0j3Ei5oubncXrxmbxKY7i0Txb7cefjIuYoU3q7jywEaGKz9vZx9tESZ/gwRJ+xvYxKDXOV15ZGRqZ7f3CGWM770un/syw0rFw/zXA6JDlhlBxnj1JdypNxkX5VBfz/KwjdcGvjEqog5SaiGlTlaeyXXkCwZ25kxgco2ZsznICASAABAAAkDARwA0xocCdoAAEAACQCDEBEBjQgwUzAEBIAAEgICPAGiMDwXsAAEgAASAQIgJgMaEGCiYAwJAAAgAAR8B0BgfCtgBAkAACACBEBP4/90IcNC8DoONAAAAAElFTkSuQmCC"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.7 MatMul节点  \n",
    "矩阵乘积称为MatMul节点。考虑$y=xW$这个计算。这里，$x,W,y$的形状分别是$1\\times D,D\\times H,1\\times H$。如下图所示：  \n",
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "上图中，损失函数$L$关于x的导数为：  \n",
    "$$\\frac{\\partial L}{\\partial x}=\\frac{\\partial L}{\\partial y}W^T$$"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "对矩阵乘积的计算$y=xW$。考虑`mini-batch`处理，假设x中保存了N笔数据。此时，x,W,y的形状分别是$N\\times D,D\\times H,N\\times H$，反向传播的计算图如下：  \n",
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "通过确认矩阵的形状，可以推导矩阵乘积的反向传播的数学式。这样就推导出了MatMul节点的反向传播。  \n",
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "关于MatMul层的实现，参加`common.layers.py`"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "da",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
